Average Error: 0.0 → 0.0
Time: 5.3s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{0.5}{e^{im}} \cdot \sin re + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \sin re\right)\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\frac{0.5}{e^{im}} \cdot \sin re + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \sin re\right)\right)
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (+
  (* (/ 0.5 (exp im)) (sin re))
  (* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (sin re))))))
double code(double re, double im) {
	return (0.5 * sin(re)) * (exp(0.0 - im) + exp(im));
}
↓
double code(double re, double im) {
	return ((0.5 / exp(im)) * sin(re)) + (sqrt(exp(im)) * (sqrt(exp(im)) * (0.5 * sin(re))));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in_binary640.0

    \[\leadsto \color{blue}{e^{-im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5}{e^{im}} \cdot \sin re} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt_binary640.0

    \[\leadsto \frac{0.5}{e^{im}} \cdot \sin re + \color{blue}{\left(\sqrt{e^{im}} \cdot \sqrt{e^{im}}\right)} \cdot \left(0.5 \cdot \sin re\right)\]

  8. Applied associate-*l*_binary640.0

    \[\leadsto \frac{0.5}{e^{im}} \cdot \sin re + \color{blue}{\sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \sin re\right)\right)}\]

  9. Final simplification0.0

    \[\leadsto \frac{0.5}{e^{im}} \cdot \sin re + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \sin re\right)\right)\]

Reproduce

herbie shell --seed 2021174 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))